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arXiv · 2209.06607

Constrained instanton approximation of Skyrmions with massive pions

Alberto García Martín-Caro
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Abstract

We present the idea of using the holonomy along a line of a constrained instanton solution (an approximate solution of the Euclidean equations of motion subject to a constraint) of an $\rm SU(2)$ Yang-Mills-Higgs theory to approximate the Skyrmion solution in a chiral model with massive pions. The fact that the gauge field acquires a nonzero mass due to the Higgs mechanism implies that a constrained instanton decays exponentially far from its center, and so does the Skyrmion configuration that it generates via the Atiyah-Manton construction. This is precisely the desired behavior at large distances for the true Skyrmion solutions when the pion mass is included.

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Alberto García Martín-Caro. 2022-10-24. Constrained instanton approximation of Skyrmions with massive pions. https://doi.org/10.1016/j.physletb.2022.137532

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